Pyramid schemes or Ponzi schemes show exponential growth by providing high profits for a few initial investors and losses among great numbers of investors.

Exponential growth models of physical phenomena only apply within limited regions, as unbounded growth is not physically realistic. Although growth may initially be exponential, the modelled phenomena will eventually enter a region in which previously ignored negative feedback factors become significant (leading to a logistic growth model) or other underlying assumptions of the exponential growth model, such as continuity or instantaneous feedback, break down.

That is the core of my argument, that most standard economic analysis fails to take into account where the assumptions that support exponential analysis break down.